Seebeck coefficient in silicon nanowire arraysEmiljana Krali and Zahid A. K. Durrani Citation: Applied Physics Letters 102, 143102 (2013); doi: 10.1063/1.4800778 View online: http://dx.doi.org/10.1063/1.4800778 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/102/14?ver=pdfcov Published by the AIP Publishing Advertisement:

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Seebeck coefficient in silicon nanowire arrays

Emiljana Krali and Zahid A. K. Durrania)

Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus,London SW7 2AZ, United Kingdom

(Received 15 October 2012; accepted 25 March 2013; published online 8 April 2013)

We measure the Seebeck coefficient S in large arrays of lightly doped n-Si nanowires (SiNWs). Our

samples consist of �107 NWs in parallel, forming a “bulk” nano-structured material. We find that

the phonon drag component of S, a manifestation of electron-phonon scattering in the sample, is

heavily suppressed due to surface scattering, and that there is a “universal” temperature dependence

for S. Furthermore, at room temperature, S is enhanced in the arrays by up to �3 times in

comparison to bulk Si. VC 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4800778]

In recent years, there has been great interest in thermo-

electric (TE) effects1–4 for application in alternative “clean”

energy sources and for more efficient utilisation of energy.

TE materials, where a temperature difference DT is converted

into an electric potential difference DV, are quantified

using the dimensionless figure-of-merit5 ZT ¼ S2rT/j, where

S ¼ DV/DT, r, and j are the Seebeck coefficient, electrical

and thermal conductivity, respectively, at temperature T. A

value of ZT� 1 is necessary for practical applications.6

While conventional bulk TE materials such as Bi2Te3 require

a compromise between S, r, and j, limiting ZT� 1, in nano-

structured materials these parameters may be varied quasi-in-

dependently3,4,7,8 such that ZT> 1. Here, S can be increased

by quantum confinement of electrons without excessively

affecting r and furthermore, j may be reduced independently

of the other parameters by either increased surface scattering

of phonons or modification of the density-of-states.7,9 As

these effects depend primarily on the length scale, there is

greater freedom in material choice, and TE devices in materi-

als even with nominally poor ZT become feasible.

Bulk Si, the most widely used semiconductor and the ba-

sis of large-scale integrated circuits, has a poor ZT� 0.01,

due to high thermal conductivity,10 j ¼ 150 W/mK at 300 K.

However, measurements on a single3 Si nanowire (SiNW)

and�100 SiNWs in parallel4 have reported ZT � 1. Here, the

NWs were defined in heavily doped (1019–1020/cm3) material

to maximise r, and j was strongly reduced �1 W/mK, either

due to increased surface scattering3 or thermoelastic effects.4

These observations demonstrate the potential for Si TE devi-

ces, raising the possibility of increased functionality in Si,

and direct integration of TE and electronic devices for energy

scavenging.

In this paper, we measure the temperature dependence of

S in samples consisting of �107 vertically aligned SiNWs

(Fig. 1) fabricated using metal-assisted chemical etching

(MACE).11,12 The process creates SiNWs from�30 to 400 nm

in diameter, with large aspect ratio up to 1:3000. We use a tran-

sient temperature and voltage measurement technique, allow-

ing direct measurement of S in thin (1 mm thickness) samples.

We also use lightly doped (�1015/cm3) n-type Si to reduce im-

purity scattering of electrons and phonons. At low doping

levels, phonon drag is the dominant contribution to S at moder-

ate to low temperatures10 (�200–30 K). Unlike heavily doped

SiNWs used in previous work,3,4 our low doping levels disen-

tangle impurity scattering from surface scattering and leave

the NW dimensions as the main source of scattering.

The SiNWs (Fig. 1) were synthesised from a lightly

doped n-type silicon (100) wafer (resistivity q� 1-5 X cm,

phosphorous doping from 5� 1014 to 3� 1015/cm3) using a

two-step chemical etching process.13,14 Here, an electroless

deposition (galvanic exchange) process deposits Ag nanopar-

ticles from HF/AgNO3/H2O solution on the Si surface. The

nanoparticles act as catalysts for subsequent etching of the

NWs in HF/H2O2/H2O solution. The main part of Fig. 1

shows the cross-section through a 60 lm long SiNW array.

The insets 1-3 show higher resolution images of three areas

(circled), at �5, �30, and �60 lm depth. The NWs are verti-

cally aligned, with parallel sidewalls over the full etch depth.

Inset 3 shows the base of the array, where NWs join the un-

etched substrate, cleaved at an angle to the NW cross-section.

The NW morphology is complex, with irregular cross-

section. This consists of a columnar core �100–400 nm in

width with vertically aligned attached ribs �30–100 nm in

width. At least some of the ribs are poorly attached or may be

FIG. 1. Main image: Cross-sectional scanning electron micrograph through

a 60 lm long SiNW array, obtained using a Zeiss Ultra Plus SEM. SiNWs

marked “A” and “B” are �100 nm and �50 nm wide. The scale bar is

10 lm. Insets 1–3 show high-resolution micrographs of the corresponding

circled regions. The scale bar is 200 nm. Inset 4 shows a broken-off section

from the top of the array. The scale bar is 100 nm.a)Electronic mail: z.durrani@imperial.ac.uk

0003-6951/2013/102(14)/143102/4/$30.00 VC 2013 American Institute of Physics102, 143102-1

APPLIED PHYSICS LETTERS 102, 143102 (2013)

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pinched-off, e.g., the NWs marked “A” (diameter �100 nm)

and “B” (diameter �50 nm) may have broken off from a

wider section. In each of our 0.5 � 0.5 cm2 samples, using an

array filling factor of �30% and an average NW diameter of

�250 nm, there are �107 NWs. The filling factor was

extracted by measuring the change in sample weight after

oxidation. Samples were oxidised at 1050 �C for several

hours, completely oxidising the NWs. The change in sample

weight allowed extraction of the weight of NWs. Using the

NW weight, length, and density of Si, it is then possible to

obtain the total cross-section area through the NWs and

hence, the filling factor.

Insets 1-3 allow comparison of the NW surface rough-

ness with array depth. This reduces from �10 to 20 nm near

the top (inset 1), to �5 nm at �30 lm depth (inset 2), to a

negligible value at the bottom (inset 3). This suggests that

the longer a section of NW surface remains immersed in the

etchant, the greater the surface roughness due to increased

surface etching. Inset 4 shows a broken-off section from

the top of the array. While the NW surface roughness is

�20 nm, the core is unaffected.

S is measured using a transient temperature and voltage

technique, allowing characterisation of thin, large area sam-

ples. In contrast, equilibrium measurements require large

separation between the hot and cold ends of the sample to

allow DT to be maintained.15–17 In previous work,3,4 single

or small numbers of SiNWs were used, such that the thermal

resistance was large and DT could be established at equilib-

rium. As we characterise �107 NWs in parallel, the thermal

resistance is reduced, making equilibrium measurements dif-

ficult. Figure 2(a) shows our experimental apparatus sche-

matically. The Si sample is sandwiched between a bottom

(cold) Cu heat sink (temperature T1) and a top Cu “hot” res-

ervoir (temperature T2), allowing measurement of the tem-

perature difference DT ¼ T2 � T1. Pressure is applied to the

top Cu block, and Al foil (thickness 120 lm) is used to

improve the Si/Cu thermal contacts. Reduction of the bottom

Cu block temperature, and the time lag in the top Cu block

reaching this temperature, allows a small transient DT to

exist across the sample. We then measure simultaneously DTand DV (open circuit voltage), as a function of time, from the

point where T1 is constant. Measurements are performed

from 300 to 30 K. The temperature sensor at the top Cu

block is placed very close (<1 mm) to the sample, allowing

measurement of temperature near the sample/Cu interface.

In addition, the time constants of the exponential decays for

DV and DT are similar and very long (�10 s or greater). The

electron distribution can then adjust as the temperature

changes, and quasi-static conditions exist in the sample. This

allows the use of equilibrium equations to quantify S. We

have also performed equilibrium measurements on the NWs

at room temperature, which give similar values of S to our

transient measurements. Finally, we consider the suitability

of the top Cu block as a heat reservoir. The heat capacity of

Cu � 24 J/mol K (Ref. 18) and of Si is �20 J/mol K (Ref.

19). The mass of the Cu block is 1 g and of the Si sample is

0.1 g. It then follows that the heat stored in the top Cu block

is �9 times greater than in the Si sample.

Figure 2(b) shows measurements for the bulk “parent”

Si sample at 160 K. DV and DT decay exponentially, with

similar time constants �16 s. S¼DV/DT is then calculated

from the DV-DT plot slope. Figure 2(b) (inset) shows linear

DV-DT plots for this sample from 280 to 80 K. Figure 2(c)

shows similar plots for an 80 lm SiNW sample, from 270 to

FIG. 2. (a) Schematic diagram of experi-

mental apparatus. The bottom and top Cu

block temperatures are T1 and T2, with

temperature difference DT ¼ T2 � T1.

Voltage difference between the blocks DV¼ V2 � V1. (b) DV and DT vs. time for

bulk Si, at 160 K. Inset shows DV � DT,

for 280–80 K heat sink temperature.

Curves are offset for clarity. (c) DV � DTfor 80 lm SiNWs, from 270 to 150 K.

Curves are offset for clarity. Inset shows

the exponential decay of DT as a function

of time, for bulk Si and SiNW samples at

160 K. (d) Seebeck coefficient for bulk

Si and for SiNW arrays with 35, 80, and

350 lm NW length. The solid lines are a

polynomial fits to provide a guide to

the eye.

143102-2 E. Krali and Z. A. K. Durrani Appl. Phys. Lett. 102, 143102 (2013)

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150 K. The inset shows DT as a function of time for bulk and

SiNW samples at 160 K. Figure 2(d) shows S for bulk Si

(Sbulk) and for SiNW arrays (SNW) with 35, 80, and 350 lm

NW lengths. Measurements were from 290 to 30 K for bulk

Si and 300–140 K for SiNWs.

In Figure 2(d), SNW is calculated as follows. We define

the equations

DTNW

DT¼ 1

1þ DTbulk=DTNW; (1)

DTbulk /1

jB

LB

AB; DTNW /

1

jNW

LNW

F� AB; (2)

DVNW

DV¼ 1

1þ DVbulk=DVNW¼ 1

1þ SbulkDTbulk=SNWDVNW;

(3)

where (DVNW, DTNW) and (DVbulk, DTbulk) are the voltage

and temperature across the SiNWs and the bulk Si substrate,

respectively. Furthermore, (jB, LB) and (jNW, LNW) are the

thermal conductivity and length in the bulk Si and SiNWs,

respectively, AB is the bulk Si surface area, and F is the fill-

ing factor of the SiNW array. In our case, F ¼ 30%, while

for jNW and jB, we use data from literature.3,10 Here, jNW is

used only to estimate DT across the SiNW and the bulk sub-

strate. In principle, a transient method allows direct measure-

ment of jNW. However, this would require an estimate of the

heat loss from the top Cu block, e.g., through the leads con-

necting to the block and the temperature sensor. The time

constants for bulk (sB) and the SiNWs (sSiNW) are very dif-

ferent, with sB ¼ 16.8 and sSiNW ¼ 44.12 (Fig. 2(c) inset).

The ratio of the time constants sB/sSiNW / jSi=jNW suggests

that jNW is reduced to �0.38jSi, a value within the range

reported for SiNWs also fabricated by a MACE process.3

Substituting Eq. (3) into the ratio SNW/S ¼ (DVNW/DV)/

(DTNW/DT), where S is the Seebeck coefficient for the entire

SiNW/Si bulk sample, and solving for SNW, we have

SNW ¼ S 1� Sbulk

S

� �DT

DTNWþ Sbulk

S: (4)

Here, DT=DTNW is given by Eqs. (1) and (2), and Sbulk and Sare given by our measured data. It was not possible to

measure the SiNWs below �140 K, due to increasing

sample resistance. At room temperature, SNW> Sbulk by up to

�3 times. However, Sbulk increases and SNW decreases with

decreasing T and at lower T, SNW< Sbulk (e.g., at 220 K for

the 80 lm sample).

The increase in Sbulk is caused by strong enhancement of

phonon drag.10 The decrease in SNW then implies suppression

of phonon drag. Typically, Sbulk¼ Spþ Sd, where Sp is the

phonon drag and Sd is the electron diffusion component. In

phonon drag, momentum transfer from phonons to electrons

via electron-phonon scattering increases the number of elec-

trons reaching the cold side and therefore S. Sp is large in

lightly doped in comparison with heavily doped materials10

as in the later case, impurity scattering of phonons sup-

presses Sp.

In lightly doped bulk semiconductors, Sd is given by20,21

Sd ¼ �kB

e

EC � EF

kBTþ r þ 5

2

� �� �: (5)

Here, kB is the Boltzmann constant, EF is the Fermi energy,

EC is the conduction band energy, e is the electron charge,

and r is a scattering factor, assumed to be �0.5 if phonon

scattering of carriers dominates over impurity scattering.21

EF can be calculated using22

nd 1� 1

2exp

ED � EF

kBT

� �þ 1

� ��1 !

¼ n0 expEF � EC

kBT

� �:

(6)

Here nd is the ionised donor concentration, ED ¼ 0.045 eV is

the donor (phosphorous) energy, n0 ¼ 2ð2pm�kBT=h2Þ3=2

is the conduction band effective density of states, m* ¼ 1.08

� electron rest mass is the electron effective mass, and h is

Planck’s constant. Finally, Sp is given by20

Sp ¼ �bvplp

leT: (7)

Here, vp and lp are the velocity and mean free path of phonons

participating in phonon drag, le is the electron mobility, and bcharacterises electron-phonon interaction. At room temperature

and above, phonon-phonon interaction (Umklapp scattering) is

predominant and b � 0. This implies that Sp may be neglected

at room temperature and Sbulk � Sd. As the temperature is low-

ered, Umklapp scattering becomes increasingly difficult, lead-

ing to b> 0. At low temperatures,21 phonon-phonon

interaction is almost void and b � 1. Furthermore, as le/T�3/2

in lightly doped Si and vp may be assumed to be constant, we

have SpT�1/2 / lp, providing a means to obtain the temperature

dependence of lp from Sp.

Figure 3(a) shows Sbulk and Sd calculated using Eqs. (1)

and (2) for 1015/cm3 doping concentration, where Sbulk � Sd

� 730 lV/K at 290 K. Sbulk is, however, slightly smaller

than Sd from 220 K < T < 300 K, as we may have overesti-

mated Sd if r < �0.5 or underestimated Sbulk due to unac-

counted interface temperature drops. Sp¼ Sbulk� Sd is

extracted assuming that Sp is negligible at room temperature.

Sp increases below �250 K and �80 K, Sp > Sd (e.g., at

30 K, Sp ¼ 0.7Sbulk). The temperature dependence of lp is

found by plotting SpT�1/2 / lp vs. T on a log-log scale (Fig.

3(a) inset). We find a power-law dependence, with lp / Tn

where n¼�2.3. This is associated with the reduction in

Umklapp scattering of phonons with reducing T and is simi-

lar to published data,10 where n � 2.1. Finally, Fig. 3(b)

shows SNW, normalized to room-temperature values, vs. T.

All samples show a similar behaviour, demonstrating a

“universal” temperature dependence with NW length.

In our lightly doped NWs, impurity scattering of pho-

nons is negligible and cannot suppress phonon drag. This

leaves surface scattering due to restricted NW dimensions

and surface roughness as the likely suppression mechanism.

As lp� 1 lm in lightly doped10 bulk Si at 300 K and

increases at lower temperatures (Fig. 3(a) inset), lp is always

greater than NW diameter. Strong surface scattering of pho-

nons in the NWs then limits lp � NW diameter and

143102-3 E. Krali and Z. A. K. Durrani Appl. Phys. Lett. 102, 143102 (2013)

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suppresses Sp. This is the same underlying mechanism for

reduced j in SiNWs,3,23 implying interdependence between

SNW and j. We also observe maximum SNW � 3Sbulk at room

temperature (Fig. 2(d)). This may be attributed to either a

change in r (Eq. (1)) due to the change in scattering mecha-

nism from phonon to surface scattering or an increase in

EC�EF due to surface effects. Finally, we estimate ZT in the

NWs, at 300 K. Using the maximum SNW¼ 2300 lV/K,

jNW¼ 8 W/m K (Ref. 3), and assuming r in the NWs is

unchanged from bulk,24 we find ZTNW¼ 0.005� 150ZTbulk.

This suggests a large improvement in the TE properties of

lightly doped SiNWs compared to bulk Si.

The authors would like to acknowledge M. Green, K.

Fobelets, C. Li, and V. Stevens for useful discussions and

the financial support of the E.ON International Research

Initiative.

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FIG. 3. (a) Sbulk (measured), Sd (calculated) and Sp (extracted), vs. T in bulk

Si. The inset shows SpT�1/2 / lp, the phonon mean free path, vs. T. (b) SNW

normalized with the room-temperature values for three samples, vs. T. Sd is

shown for comparison.

143102-4 E. Krali and Z. A. K. Durrani Appl. Phys. Lett. 102, 143102 (2013)

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